Understanding the Relationship
The energy of a photon (E) is related to its wavelength (λ) by the following equation:
* E = hc/λ
where:
* E = energy of the photon (in Joules)
* h = Planck's constant (6.626 x 10^-34 J·s)
* c = speed of light (3 x 10^8 m/s)
* λ = wavelength of the photon (in meters)
Solving for Wavelength
1. Rearrange the equation to solve for λ:
λ = hc/E
2. Plug in the values:
λ = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (1.06 x 10^-19 J)
3. Calculate the result:
λ ≈ 1.87 x 10^-6 meters
Converting to a More Convenient Unit
It's often more convenient to express wavelength in nanometers (nm):
1.87 x 10^-6 meters * (10^9 nm / 1 meter) ≈ 1870 nm
Therefore, the wavelength of a photon with an energy of 1.06 x 10^-19 Joules is approximately 1870 nanometers.
